In ideal gas dynamics temperature appears as an intensive variable $T$ connected to internal energy $e$ and density $\rho$ by
- $T=\frac{e}{\rho}$
- $p=\gamma e$
towards understanding by critical constructive inquiry
In ideal gas dynamics temperature appears as an intensive variable $T$ connected to internal energy $e$ and density $\rho$ by
Cosmic Microwave Background Radiation CMB is supposed to be an afterglow of a Big Bang which started with Cosmic Inflation as a theory proposed by theoretical physicist Alan Guth as an extremely rapid expansion from a Universe of the size of a proton to the size of a pea taking place during a period of time from $10^{-36}$ to $10^{-32}$ seconds after zero time with an expansion factor of $10^{13}$.
A common view is that Alan Guth's theory solves all three main problems of cosmology: the horizon problem, the flatness problem and the magnetic monopole problem.
The Nobel Prize in Physics 2023 was awarded for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter, with an attosecond = $10^{-18}$ second.
Visible light has time scale of $10^{-15}$, x-rays $10^{-18}$ and $\gamma$-rays $10^{-22}$ seconds as real physics with highest frequency presently known. Frequency is connected to energy through Planck's Law which allows determining the frequency of $\gamma$-rays by measuring the energy of $\gamma$-radiation.
Cosmic Inflation is described follows in popular form:
Measuring temperature accurately is a delicate procedure. |
You can measure your body temperature by body contact with a quicksilver thermometer or at distance by an infrared thermometer. Both work on a principle of thermal equilibrium between source and thermometer sensor as a stable state over time. Your body is assigned the temperature recorded by the thermometer.
Temperature can be seen as a measure of energy in the form of heat energy or vibrational energy of a vibrating system like an atomic lattice as the generator of radiation as radiative heat transfer.
Computational Blackbody Radiation offers a new analysis of radiative heat transfer using classical wave mechanics as a deterministic form of Planck's analysis based on statistics of quanta. The basic element of the analysis is a radiation spectrum from a vibrating atomic lattice:
Man-made Universality of Shape |
This is a clarification of the previous post on the perfect Planck blackbody spectrum of the Cosmic Microwave Background Radiation CMB as a 14 Billion years afterglow of Big Bang as the leading narrative of cosmology physics today. See also this recent post and this older illuminating post.
The Planck spectrum as the spectrum of an ideal blackbody, takes the formThe Cosmic Microwave Background radiation CMB is supposed to be a 14 billion year after-glow with perfect Planck blackbody spectrum at temperature $T=2.725$ Kelvin K of a Universe at $T=3000$ K dating back to 380.000 years after Big Bang. The apparent 1000-fold temperature drop from 3000 to 3 K is supposed to be the results of an expansion and not cooling.
To get an idea of the magnitude of CMB let us recall that a Planck spectrum at temperature $T$ stretches over frequencies $\nu\sim T$ and reaches maximum radiation intensity $E\sim T^3$ near the end with a high frequency cut-off over an interval $\frac{\nu}{T}\sim 1$ (notice exponential scale):
The $10^3$-fold temperature drop thus corresponds to a $10^9$ decrease of maximum intensity and $10^3$ decrease in spectrum width. Intensity over width decreases with a factor $10^6$ as a measure of precision in peak frequency.
We understand that to draw conclusions concerning a 3000 K spectrum from a measured 3 K spectrum requires a very precision on the level of microKelvin or 0.000001 K. Is this really possible? Is it possible to reach the precision 2.725 K from intensity maximum?
Why is modern physics focussed on measuring quantities which cannot be measured, like ghosts?
CMB was first detected as noise maybe from birds visiting antennas, but the noise persisted even after antennas were cleaned and then the conclusion was drawn that CMB must be left-over from Big Bang 14 billion years ago and not from any birds of today. Big Bang is physics, while birds is ornithology.
Classical physics peaked in the late 19th century with Maxwell's equations aiming to describe all of electromagnetics as a form of continuum wave mechanics, but crumbled when confronted with the Ultra-Violet Catastrophe UVC of heat radiation from a body of temperature $T$ scaling like $T\nu^2$ with frequency $\nu$ threatening to turn everything into flames without an upper bound for frequencies, because wave mechanics did not seem to offer any escape from UVC.
Planck took on role of saving physics from looming catastrophe, but could not find a resolution within deterministic wave mechanics and so finally gave up and resorted to statistical mechanics with high frequencies less likely in the spirit of Boltzmann's thermodynamics and 2nd Law with order less likely than disorder.
There is thus a close connection between UVC and 2nd Law. Boltzmann would say that the reason we do not experience UVC is that high frequencies are not likely, but the physics of why is missing. Explaining that UVC is not likely would no explain why there is not any observation UVC whatsoever.
I have followed a different route replacing statistics by finite precision physics for UVC (and similarly for 2nd Law), where high frequencies with short wave length cannot be radiated because finite precision sets a limit on the frequencies an atomic lattice can carry as coordinated synchronised motion. In this setting UVC can never occur.
A basic mission for a 2nd Law is thus to prevent UVC. This gives 2nd Law deeper meaning as a necessary mechanism preventing too fine structures/high frequencies to appear and so cause havoc. 2nd Law is thus not a failure to maintain order over time, but a necessary mechanism to avoid catastrophe from too much order.
Similarly, viscosity and friction appear as necessary mechanisms destroying finite structure/order in order to let the World to continue, and so not only as defects of an ideal physics without viscosity and friction. This is the role of turbulence as described in Computational Turbulent Incompressible Flow and Computational Thermodynamics.
We can compare with the role of interest rate in an economy with zero interest rate of an ideal economy leading to catastrophe over time. If there is no cost of getting access to capital, any crazy mega project could get funding and catastrophe would follow. This was the idea 2008-2023 preceding the collapse predicted to 2025. Too little friction makes the wheels turn too fast. Too much idealism leads to ruin.
A main challenge to physicists at the turn to modernity 1900 was to explain radiative heat transfer as the process of emission, transfer and absorption of heat energy by electromagnetic waves described by Maxwell's equations. The challenge was to explain why real physics avoids an ultra-violet catastrophe with radiation intensity going to infinity with increasing frequency beyond the visible spectrum.
More precisely, the challenge was to uncover the physics of a blackbody spectrum with radiation intensity scaling with $T\nu^2$ with $T$ temperature and frequency $\nu\le\nu_{max}$ with $\nu_{max}$ a cut-off frequency scaling with $T$, and intensity quickly falling to zero above cut-off.
Planck as leading physicist of the German Empire took on the challenge and after much struggle came up with an explanation based on statistics of energy taking the above form as Planck's Law, which has served into our time as a cover up a failure to explain a basic phenomenon in physical terms.
Computational Blackbody Radiation offers an explanation in terms of finite precision physics setting a cut-off (scaling with temperature) on the frequency of emission from coordinated oscillations of an atomic lattice, with uncoordinated atomic motion stored as heat energy.
In this analysis heat is transferred from a body of higher temperature to a body of lower temperature through a resonance phenomenon analogous to the resonance between two tuning forks. The essence can be described in terms of a forced acoustically weakly damped harmonic oscillator:
The idea about the Cosmic Microwave Background CMB radiation is conveyed to the public by authoritative sources as follows starting at the creation of the Universe with a Big Bang:
Modern physics appears as a form of homeopathy in reverse. A main idea of homeopathy is to obtain a major health effect from a very very diluted form of some substance, the smaller the better. The characteristic of modern physics, as rather the opposite, is identification of a very small effect from a very very large cause as in the following key examples with increasing presence in later years (with year of Nobel Prize in Physics):
This is a continuation of a previous post on the same topic. The European Space Agency ESA sends this message to the people of Europe and the World:
CMB spectrum as perfect Planck blackbody spectrum. But low frequencies in the far infrared spectrum are missing! |
For when propositions are denied, there is an end
of them, but if they bee allowed, it requireth a
new worke. The Essais of Sr. Francis Bacon, London, 1612
The further a society drifts from the truth, the more it will hate those who speak it. George Orwell
Nothing is created by coincidence, rather there is reason and necessity for everything. Leukippus, 5th Century BC.
De Omnibus Dubitandum